An Algebraic Approach to Canonical Formulas: intuitionistic Case

@article{Bezhanishvili2009AnAA,
  title={An Algebraic Approach to Canonical Formulas: intuitionistic Case},
  author={Guram Bezhanishvili and Nick Bezhanishvili},
  journal={Rew. Symb. Logic},
  year={2009},
  volume={2},
  pages={517-549}
}
We introduce partial Esakia morphisms, well partial Esakia morphisms, and strong partial Esakia morphisms between Esakia spaces and show that they provide the dual description of (∧,→)-homomorphisms, (∧,→, 0)-homomorphisms, and (∧,→,∨)-homomorphisms between Heyting algebras, thus establishing a generalization of Esakia duality. This yields an algebraic characterization of Zakharyaschev’s subreductions, cofinal subreductions, dense subreductions, and the Closed Domain Condition. As a consequence… CONTINUE READING